Which of the following is an empty set?

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(B) For option $A$: $x^2 - 1 = 0 \implies x = \pm 1$,which are real numbers. So,the set is $\{-1, 1\}$.For option $B$: $x^2 + 1 = 0 \implies x^2 = -1$

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$\{x : x \in \mathbb{R} 	ext{ and } x^2 + 1 = 0\}$

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(B) For option $A$: $x^2 - 1 = 0 \implies x = \pm 1$,which are real numbers. So,the set is $\{-1, 1\}$.For option $B$: $x^2 + 1 = 0 \implies x^2 = -1$. Since the square of any real number cannot be negative,there is no real value of $x$ that satisfies this equation. Thus,this is an empty set.For option $C$: $x^2 - 9 = 0 \implies x = \pm 3$,which are real numbers. So,the set is $\{-3, 3\}$.For option $D$: $x^2 - x - 2 = 0 \implies (x-2)(x+1) = 0 \implies x = 2, -1$,which are real numbers. So,the set is $\{-1, 2\}$.Therefore,the correct option is $B$.

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